In a saucepan over medium heat, add lychees, sugar and water. Stir until all of the sugar is dissolved into the water and use a spatula to crush and break down lychees. Drop the heat to low and simmer for about 5 minutes. Remove from the heat and allow to sit so the lychees can infuse, ideally 30 minutes. When ready to use, strain to remove lychees and store in an airtight container in the refrigerator.